Find the product of the following:
$(a + b) (a^{2} + 2 a b + b^{2})$

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Solution

Product of $(a + b) (a^{2} + 2 a b + b^{2})$
$\Rightarrow a (a^{2} + 2 a b + b^{2}) + b (a^{2} + 2 a b + b^{2})$
$\Rightarrow a^{3} + 2 a^{2} b + a b^{2} + a^{2} b + 2 a b^{2} + b^{3}$
$\Rightarrow a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2} = {(a + b)}^{3}$
Hence, the answer is ${(a + b)}^{3} .$

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$The product (a + b) (a - b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})$ is equal to

Q. Question 3

Which of the following is correct?
a)

(a - b)^{2} = a^{2} + 2 a b - b^{2}

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(a - b)^{2} = a^{2} - b^{2}

(a + b)^{2} = a^{2} + 2 a b - b^{2}

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Find the product

(2 a + b + c) (4 a^{2} + b^{2} + c^{2} - 2 a b - b c - 2 c a)

Question 84 (ix)

Simplify

$(a - b) (a^{2} + b^{2} + a b) - (a + b) (a^{2} + b^{2} - a b)$

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Find the product of the following:(a+b)(a2+2ab+b2)

Product of (a+b)(a2+2ab+b2)⇒a(a2+2ab+b2)+b(a2+2ab+b2)⇒a3+2a2b+ab2+a2b+2ab2+b3⇒a3+b3+3a2b+3ab2=(a+b)3Hence, the answer is (a+b)3.

Find the product of the following:
$(a + b) (a^{2} + 2 a b + b^{2})$

Product of $(a + b) (a^{2} + 2 a b + b^{2})$
$\Rightarrow a (a^{2} + 2 a b + b^{2}) + b (a^{2} + 2 a b + b^{2})$
$\Rightarrow a^{3} + 2 a^{2} b + a b^{2} + a^{2} b + 2 a b^{2} + b^{3}$
$\Rightarrow a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2} = {(a + b)}^{3}$
Hence, the answer is ${(a + b)}^{3} .$